Simplify the following expression: $ n = \dfrac{-6}{-7y - 6} + \dfrac{-7}{2} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-6}{-7y - 6} \times \dfrac{2}{2} = \dfrac{-12}{-14y - 12} $ Multiply the second expression by $\dfrac{-7y - 6}{-7y - 6}$ $ \dfrac{-7}{2} \times \dfrac{-7y - 6}{-7y - 6} = \dfrac{49y + 42}{-14y - 12} $ Therefore $ n = \dfrac{-12}{-14y - 12} + \dfrac{49y + 42}{-14y - 12} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-12 + 49y + 42}{-14y - 12} $ $n = \dfrac{49y + 30}{-14y - 12}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-49y - 30}{14y + 12}$